The issue is that it's very abstract, and all the mechanics of banking are accounting operations, whereas people don't tend to think that way. The deposits themselves are entries on the liability side of the bank's balance sheet. The bank doesn't store money for customers, they take whatever asset you give them and give you basically an IOU in return. So the "customer deposit" is not what you gave the bank (say if you deposited cash), it's a number in a database. Just like what is 'in' the bank's exchange settlement accounts at the central bank (e.g. Federal Reserve), and just like what is moved around in international finance. Electronic messages representing IOUs.
This is balanced by a mix of assets, which are a whole number of things. A tiny amount of cash, a small amount of central bank reserves, some in treasuries and bonds, and the assets created by the bank loans, etc.. (When the bank creates those loans, they create new deposits and a new asset in the loan, in equal amounts. So the assets and liabilities of the bank increase but the balance is zero).
So if the bank gets in trouble, it's because some of the asset mix has declined in value (like too many people have defaulted on their loans) to the point that the assets no longer cover those liabilities.
No, the amount they can lend out is mostly based on their capital. If they want to lend money out but they have reached their capital adequacy limit, they have to capital raise by issuing new shares for cash, not seek more deposits. (I’ve been a bank shareholder when they had to do this, when the Basel III rules changed the limits to make things more stable).
Deposits are liquidity that help grease the wheels, so it’s necessary, but it’s actually more the transfers of money moving in and out that they need, not liabilities sitting on their balance sheets.
This is balanced by a mix of assets, which are a whole number of things. A tiny amount of cash, a small amount of central bank reserves, some in treasuries and bonds, and the assets created by the bank loans, etc.. (When the bank creates those loans, they create new deposits and a new asset in the loan, in equal amounts. So the assets and liabilities of the bank increase but the balance is zero).
So if the bank gets in trouble, it's because some of the asset mix has declined in value (like too many people have defaulted on their loans) to the point that the assets no longer cover those liabilities.